Re: entangled states

"Igor Khavkine" <igor.kh@xxxxxxxxx> schrieb
> You have one right idea: simultaneity is only defined in special
> relativity when a reference frame is specified. Thus, as you've pointed
> out, when two measurements are made on space-like separated components
> of an entangled system, each measurement can be seen as made either
> before or after the other, depending on the frame of reference.
> Together with the principle of causality, this should give you a hint
> that nothing is actually transfered from the location of one
> measurement to the other.

A wrong hint. The situation can indeed be interpreted in two ways:
t(A) < t(B) and (for another choice of t) reverse. (From point of
view of Lorentz/Poincare two hypotheses about the actual
state of motion of the ether.)
But the description what _actually_ happens can,
of course, also depend on this _actual_ state, therefore,
depend on the choice of t. Thus, for every t we have an explanation:
A->B resp. (for the other choice of t) B->A.

(Bohmian mechanics, which depends on a preferred frame, gives
you an example of this scheme. BM1, using t1 as the preferred
frame, gives the deterministic, causal in t1, explanation A->B,
BM2, using t2 as the preferred frame, gives another deterministic
but causal in t2 explanation.)

Two explanations (and, as a consequence, no possibility to
use the effect for FTL information transfer, because each use
would contradict one of the explanations), but all
explanations violate Einstein causality. If something is wrong
in every realistic explanation it is wrong.

> But you do have one idea wrong: correlation does not imply causation.

Of course, but the correlations used in Bell's inequality are very
special ones, between the results of the measurements m_A, m_B
as well as the control parameters (choices of the experimenters)
c_A, c_B.

> Quantum mechanics predicts that the outcomes of two measurements
> performed on an entangled system may be correlated (knowing one will
> tell you the other, and vice versa). However, it says nothing about one
> measurement causing the outcome of another measurement.

No, the violation of Bell's inequality tells a lot, at least if we accept
the
necessity of realistic explanations. (Else, using phrases like
"nothing is _actually_ transfered", as you do, would be meaningless.)

> Especially, if
> the two measurements are space-like separated, the ambiguity in their
> temporal ordering should be enough to make the lack of such predictions
> from QM self evident.

It is far away from being self-evident. The violation of Bell's
inequality has to be considered as a classical example
of an indirect observation of a violation of Einstein causality:
Every reasonable explanation contains a violation of Einstein
causality.

> If we have to measurements, A and B, correlation is a symmetric
> relationship. If A is correlated with B, then B is correlated with A.
> On the other hand, causation is only one-way. If A causes B, then B
> does not cause A. QM predicts a symmetric relationship between the
> measurements, hence it can only refer to correlation.

The claim "There exists a causal connection A->B or B->A" (which
is the realistic consequence of violations of Bell's inequality) is
symmetric in A and B but refers to causation.

A correlation requires explanation. Realists accept three types of
explanations: A->B; B->A; C->A and C->B (common cause).
Bell's inequality excludes the common cause. A->B or B->A
remains.

For non-realists we have, instead, four explanations:
A->B; B->A; C->A and C->B; a quantum miracle happens.

> On the other
> hand, there is nothing in special relativity that prevents correlation
> at space-like separations, it only imposes restrictions on causation.

In a realistic interpretation, Einstein causality forbids violations of
Bell's inequality.

Ilja

.

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